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- W4300650541 abstract "We give a simple geometric proof that $e$ is irrational, using a construction of a nested sequence of closed intervals with intersection $e$. The proof leads to a new measure of irrationality for $e$: if $p$ and $q$ are integers with $q > 1$, then $|e - p/q| > 1/(S(q)+1)!$, where $S(q)$ is the smallest positive integer such that $S(q)!$ is a multiple of $q$. We relate this measure for $e$ to a known one and to the greatest prime factor of an integer. We make two conjectures and recall a theorem of Cantor that can be proved by a similar construction." @default.
- W4300650541 created "2022-10-03" @default.
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- W4300650541 date "2007-04-10" @default.
- W4300650541 modified "2023-10-16" @default.
- W4300650541 title "A geometric proof that $e$ is irrational and a new measure of its irrationality" @default.
- W4300650541 doi "https://doi.org/10.48550/arxiv.0704.1282" @default.
- W4300650541 hasPublicationYear "2007" @default.
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